trig substitutions

I have having trouble doing this one:
integral of radical(x^2 + 4)dx
I set x = tan(u)
dx = sec^2(x)du
here is what i did:
integral of radical(4tan^2(u) + 4)
Pulled out a radical 4
integral of 2tan(u)
this equals 2sec^2(u) + C
sec(u) in this scenario is (x+2)/(2) since tan(u) = x/2
I did this then:
2((x+2/2))^2
The answer after doing this isnt the same in the book
I am suppose to get: 1/2xradical(x^2 + 4) + 2ln(x + radical(x^2 + 4)) + C

I have having trouble doing this one:
integral of radical(x^2 + 4)dx
I set x = tan(u)
dx = sec^2(x)du
here is what i did:
integral of radical(4tan^2(u) + 4)
Pulled out a radical 4
integral of 2tan(u)
this equals 2sec^2(u) + C
sec(u) in this scenario is (x+2)/(2) since tan(u) = x/2
I did this then:
2((x+2/2))^2
The answer after doing this isnt the same in the book
I am suppose to get: 1/2xradical(x^2 + 4) + 2ln(x + radical(x^2 + 4)) + C

The number in red above is an error. And I more or less can't follow what you did after that. So....